Bridge missing monitoring data restoration method based on E-VMD and SSA-GRU combined model

Abstract

The invention discloses a bridge missing monitoring data restoration method based on an E-VMD and SSA-GRU combined model, and belongs to the technical field of bridge missing monitoring data restoration, and the method comprises the following steps: S1, data collection and preprocessing; s2, constructing and training a model; and S3, missing data restoration. According to the method, the bridge structure response is accurately obtained through the E-VMD, the calculation efficiency is improved, the frequency component is positioned more accurately, and the processing capacity of nonlinear signals is enhanced. In order to solve the influence of the unreasonable value of the hyper-parameter on the GRU performance, the key parameters in the GRU neural network are optimized by using the sparrow search algorithm, so that the robustness and generalization ability of the model are greatly improved, and the repair result is more accurate and higher in precision.

Description

Technical Field

[0001] This invention relates to the field of bridge missing monitoring data repair technology, specifically to a method for bridge missing monitoring data repair based on a combined E-VMD and SSA-GRU model. Background Technology

[0002] Bridge health monitoring systems collect real-time structural response data (such as strain, deflection, acceleration, and temperature) from various sensors, providing crucial information for bridge health assessment and operational maintenance. However, due to the long-term exposure of bridges to complex environments, sensors are susceptible to environmental interference, equipment aging, and data transmission errors, leading to abnormal data types such as missing data, noise, and drift. These abnormal data not only affect the accuracy of bridge health assessments but may also lead to erroneous maintenance decisions, ultimately threatening the safe operation of the bridge. Therefore, how to quickly and accurately correct outliers in bridge monitoring data and ensure its accuracy and reliability has become one of the key issues urgently needing to be addressed in the field of bridge health monitoring.

[0003] The types of bridge anomaly monitoring data mainly include noise, gain, accuracy degradation, drift, trends, missing data, outliers, and overrange oscillations. For these types of anomaly data, scholars both domestically and internationally have proposed various targeted processing methods, which can be mainly categorized into methods based on statistics, signal processing, machine learning, and deep learning. Zhou Hailiang et al. proposed a method using Lagrange interpolation to handle the problem of missing bridge deflection monitoring data, while Ren Pu proposed a method based on one-dimensional time history interpolation and fitting to repair bridge anomaly monitoring data. Currently, deep learning models such as Long Short-Term Memory (LSTM) networks and gated recurrent units (GRUs) have gradually attracted the attention of many scholars due to their excellent performance in processing time series data, and have gradually become a research hotspot in bridge anomaly data repair methods. Ju Hanwen et al. used a reconstructed GRU neural network to repair bridge structural anomaly monitoring data. Through experimental comparison, they found that GRU outperforms traditional BP (BackPropagation) neural networks and Long Short-Term Memory (LSTM) neural networks in prediction accuracy.

[0004] However, existing research methods still have several limitations. First, methods based on statistics and signal processing typically rely on the linear assumption of the data, and their ability to process complex nonlinear bridge monitoring data needs improvement. The bridge operating environment is usually very complex, and the monitored data is often nonlinear. Second, signal processing methods (such as Fourier transform and wavelet transform) are prone to mode aliasing when processing nonlinear signals, i.e., signals of different frequency components are intertwined and disordered, leading to inaccurate signal decomposition and an inability to obtain accurate responses from the bridge structure. While deep learning models (such as LSTM and GRU) show satisfactory performance in processing time series data, the determination of their internal hyperparameters (such as the number of hidden layer units and the learning rate) often relies on human experience and traditional trial-and-error methods, lacking systematic optimization strategies, resulting in unstable overall model performance.

[0005] To address the issue of missing massive strain data in bridge health monitoring systems due to environmental interference or sensor malfunctions, this paper proposes a method for repairing missing bridge monitoring data based on a combined E-VMD and SSA-GRU model. Summary of the Invention

[0006] The technical problem to be solved by this invention is: how to solve the problem of missing massive strain data in bridge health monitoring systems due to environmental interference or sensor failure, reconstruct the missing bridge monitoring data, and achieve accurate repair. This invention provides a method for repairing missing bridge monitoring data based on a combined E-VMD and SSA-GRU model.

[0007] like Figure 10 As shown, the present invention solves the above-mentioned technical problems through the following technical solution, and the present invention includes the following steps:

[0008] S1: Data Acquisition and Preprocessing

[0009] Collect bridge anomaly monitoring data of a preset type, and divide the bridge anomaly monitoring data into training set and test set according to a set ratio;

[0010] S2: Model Building and Training

[0011] A combined model based on E-VMD and SSA-GRU is constructed. The combined model based on E-VMD and SSA-GRU is trained using training set data to obtain the trained model, namely the bridge missing monitoring data repair model. In the combined model based on E-VMD and SSA-GRU, the actual structural response data of the bridge in the bridge anomaly monitoring data is extracted by the E-VMD method, and the hyperparameters of the GRU neural network are optimized by the SSA algorithm.

[0012] S3: Missing Data Repair

[0013] After preprocessing, the real-time collected bridge anomaly monitoring data is input into the bridge missing monitoring data repair model. The bridge missing monitoring data repair model is then used to repair the data, and the repaired bridge monitoring data is output.

[0014] Furthermore, in step S1, bridge anomaly monitoring data is collected in real time by sensors of the actual bridge health monitoring system.

[0015] Furthermore, in step S2, the specific process of extracting the bridge structural response from the bridge anomaly monitoring data using the E-VMD method is as follows:

[0016] S211: The EMD method is used to adaptively decompose the preprocessed bridge anomaly monitoring data x(n) to obtain M IMF components. The correlation coefficient l1(m) between each IMF component and x(n) is calculated, and the correlation threshold l is defined. limt The correlation coefficient l1(m) is greater than or equal to the correlation threshold l. limt The preprocessed signal x0(n) is obtained by adding the IMF components, where m = 1, 2, ... M;

[0017] S212: Perform VMD decomposition on signal x0(n) under different K values. Each decomposition yields a set of narrowband IMF components. The relationship between the narrowband IMF components and the preprocessed signal x0(n) is determined by calculating the correlation coefficient l2(k). The condition l2(k) ≥ l is considered to be met. limt The narrowband IMF components are added together to obtain the reconstructed signal x1(n), where k = 1, 2, ... K;

[0018] S213: The mutual information relationship between the preprocessed signal x0(n) and the reconstructed signal x1(n) is calculated by the mutual information method to obtain the mutual information index MI. When the mutual information index MI reaches its maximum value, the corresponding K value is the number of optimal modes obtained by the variational mode decomposition of the preprocessed signal x0(n).

[0019] S214: Reconstruct all preprocessed signals x0(n) satisfying l2(k)≥l under the optimal number of modes. limt The true structural response of the bridge can be obtained by using the narrowband IMF component.

[0020] Furthermore, in step S211, the formula for calculating the correlation coefficient l1(m) is as follows:

[0021]

[0022] Relevant threshold l limt The definition is as follows:

[0023]

[0024] Where ξ is the resolution coefficient; c is an empirical constant, c k In this context, k is the index subscript used to distinguish different sequences after decomposition.

[0025] Furthermore, in step S212, the formula for calculating the correlation coefficient l2(k) is as follows:

[0026]

[0027] Among them, IMF k This refers to the k-th narrowband IMF component obtained after VMD decomposition. It represents the average value of the k-th narrowband IMF component.

[0028] Furthermore, in step S213, the formula for calculating the mutual information index MI is as follows:

[0029] MI[x1,x0]=H(x1)+H(x0)-H(x1,x0)

[0030] Where H(x1), H(x0) and H(x1,x0) are the information entropy and joint entropy of x0(n) and x1(n), respectively, defined as follows:

[0031]

[0032] in, and Let x0(n) and x1(n) be the probability mass functions and the joint probability mass function, respectively.

[0033] Furthermore, in step S2, the specific process of optimizing the hyperparameters of the GRU neural network using the SSA algorithm is as follows:

[0034] S221: Set the maximum number of iterations for the SSA algorithm, the number of hidden units, the maximum number of training rounds, and the initial learning rate for the GRU neural network, and use the root mean square error of the prediction results of the GRU neural network as the fitness function.

[0035] S222: Initialize the sparrow population;

[0036] S223: Update the positions of the discoverer, joiner, and watcher to obtain the global optimal position and best fitness;

[0037] S224: Determine if the maximum number of iterations has been reached;

[0038] S225: If the maximum number of iterations has not been reached, continue iterating and updating, and proceed to steps S223 to S224. Otherwise, output the optimization results of the number of hidden units, the maximum number of training rounds, and the initial learning rate of the GRU neural network to obtain the optimized GRU neural network.

[0039] Furthermore, in step S223, during each iteration:

[0040] The location update of the discoverer is described as follows:

[0041]

[0042] Where t is the current iteration number; j = 1, 2, 3, ..., d; iter max Indicates the maximum number of iterations; X i,j Let represent the position information of the i-th sparrow in the j-th dimension; α is a random number; R2 is the preset warning value, R2∈[0,1]; ST is the preset safety value, ST∈[0.5,1]; Q is a random number following a normal distribution; L represents a matrix of size 1×d, in which every element is 1;

[0043] The location update status of new members is described as follows:

[0044]

[0045] Among them, Xp is the optimal position currently occupied by the discoverer;

[0046] The location update status of the vigilant is described as follows:

[0047]

[0048] Among them, X best The current global optimal position; β is the step size control parameter; K is a random number, K∈[-1,1]; f i f represents the fitness value of the current individual sparrow; g f represents the current global optimum, i.e., the optimal fitness; w This represents the worst current global fitness value; ε is a constant used to avoid division by zero error.

[0049] Furthermore, in step S2, the GRU neural network controls the transmission and forgetting of information through two gating mechanisms. When the input bridge real structural response data first passes through the update gate, the fusion ratio of new information and historical information at the current moment is determined. Then, the reset gate controls the degree of influence of historical information in generating candidate hidden states. Next, the candidate hidden state is calculated and weighted and combined with the hidden state at the previous moment to generate the current hidden state, thereby completing the processing of time series information.

[0050] Furthermore, in the GRU neural network, the output formula for the update gate is as follows:

[0051] z t =σ(W z ·[h t-1 ,x t ]+b z )

[0052] Among them, z t This indicates updating the output of the gate, h. t-1 x represents the hidden state at the previous moment. t W represents the current input. z Let B be the weight matrix. z Here, σ is the bias term, and σ is the sigmoid function.

[0053] The output formula for resetting the door is as follows:

[0054] r t =σ(W r ·[h t-1 ,x t ]+b r )

[0055] Where, r t W indicates the output of the reset gate. r Let B be the weight matrix. r For bias terms;

[0056] The formula for calculating the candidate hidden state is as follows:

[0057]

[0058] in, Represents the candidate hidden state, r t ⊙h t-1 W represents element-wise multiplication. h Let b be the weight matrix. h For bias terms;

[0059] The formula for calculating the current hidden state is as follows:

[0060]

[0061] Where: h t Represents the hidden state at the current time step, 1-z t z represents the proportion of the hidden state retained from the previous time step. t This represents the proportion of candidates added to the hidden state.

[0062] The present invention has the following advantages over the prior art:

[0063] 1. By accurately acquiring the bridge structure response through E-VMD, computational efficiency was improved, frequency components were located more accurately, and the ability to process nonlinear signals was enhanced.

[0064] 2. To address the impact of unreasonable hyperparameter values ​​on GRU performance, the sparrow search algorithm was used to optimize key parameters in the GRU neural network, which greatly improved the robustness and generalization ability of the model, resulting in more accurate and precise repair results.

[0065] 3. By combining E-VMD and SSA-GRU models, a multi-layered anomaly data repair framework is achieved, fully leveraging the advantages of each component. E-VMD processes nonlinear signals, GRU captures the dependencies between time-series data, and SSA is used to optimize the GRU neural network, improving its reconstruction performance. This multi-layered optimization framework enhances the model's prediction accuracy, robustness, and generalization ability. Attached Figure Description

[0066] Figure 1 This is a schematic diagram of the structure of the GRU neural network in an embodiment of the present invention;

[0067] Figure 2 This is a flowchart illustrating the E-VMD method in an embodiment of the present invention;

[0068] Figure 3 This is a schematic diagram of the SSA optimization of the GRU neural network in an embodiment of the present invention;

[0069] Figure 4 This is a technical roadmap of the bridge missing monitoring data repair method based on the E-VMD and SSA-GRU combined model in this embodiment of the invention;

[0070] Figure 5 This is a line graph of strain monitoring data in an embodiment of the present invention;

[0071] Figure 6 This is a diagram showing the bridge structure response results extracted by E-VMD in an embodiment of the present invention;

[0072] Figure 7 This is a comparison chart of strain prediction and reconstruction results in embodiments of the present invention;

[0073] Figure 8 This is a comparison chart of the reconstruction and repair errors of strain data from different models in this embodiment of the invention;

[0074] Figure 9 This is the strain repair in the embodiments of the present invention - fitting effect of three models R 2Comparison figures: (a) is a single GRU model, (b) is a combined E-VMD and GRU model, and (c) is a combined E-VMD and SSA-GRU model.

[0075] Figure 10 This is a schematic diagram of the overall process of the bridge missing monitoring data repair method based on the E-VMD and SSA-GRU combined model of the present invention. Detailed Implementation

[0076] The embodiments of the present invention are described in detail below. These embodiments are implemented based on the technical solution of the present invention, and provide detailed implementation methods and specific operation processes. However, the scope of protection of the present invention is not limited to the following embodiments.

[0077] This embodiment provides a technical solution: a method for repairing missing bridge monitoring data based on a combined E-VMD and SSA-GRU model. First, E-VMD extracts multi-scale structural response features from bridge monitoring signals, separating noise from the actual strain components of the bridge. Second, SSA is combined with GRU hyperparameter optimization to construct a dynamic prediction model, improving the reconstruction accuracy of missing data. This forms a multi-level data repair framework that effectively extracts structural response features from bridge monitoring data and reduces the impact of environmental noise and abnormal data on the repair results. Finally, a real bridge test verifies the advancement of the proposed method and its ability to accurately achieve the expected goals.

[0078] The basic principles of the main technical means in the above-mentioned repair methods will be explained in more detail below.

[0079] I. Sparrow Search Algorithm

[0080] The Sparrow Search Algorithm (SSA) is an optimization algorithm inspired by the foraging and anti-predation behaviors of sparrows. Its main purpose is to simulate certain sparrow behaviors and apply them to optimization algorithms to solve global optimization problems, providing a novel solution method and approach for practical problems with numerous local optima.

[0081] The main roles in a sparrow population can be broadly divided into two categories: finders and joiners. Finders are responsible for locating food and providing the population with information about foraging areas; joiners utilize the finders to obtain food. In their natural state, individuals monitor each other, and joiners in a sparrow population typically compete for food resources from companions with high predation rates in order to increase their own hunting efficiency. While foraging, all individuals remain vigilant about their surroundings to guard against predators.

[0082] Suppose that a population X consisting of n sparrows is represented as:

[0083]

[0084] Where d represents the dimension of the variable in the problem to be optimized.

[0085] Then, the fitness value F of all sparrows x It can be represented as:

[0086]

[0087] Where f represents the fitness value.

[0088] The location update of the discoverer during each iteration of the algorithm is described as follows:

[0089]

[0090] Where t is the current iteration number; j = 1, 2, 3, ..., d; iter max X represents the maximum number of iterations, which is a constant; i,j Let represent the position information of the i-th sparrow in the j-th dimension; α is a random number; R2 is the preset warning value, R2∈[0,1]; ST is the preset safety value, ST∈[0.5,1]; Q is a random number following a normal distribution; L represents a matrix of size 1×d, in which every element is 1.

[0091] When R2 < ST, it means that there are no predators in the foraging environment at this time, and the discoverer can perform extensive search operations;

[0092] When R2 > ST, it means that some sparrows in the population have discovered the predator and sent a warning message to the other sparrows. At this time, all sparrows need to quickly fly to other safe areas to forage.

[0093] The location update status of new members is described as follows:

[0094]

[0095] Among them, Xp is the optimal position currently occupied by the discoverer.

[0096] The location update status of the vigilant is described as follows:

[0097]

[0098] Where X best The current global optimal position; β is the step size control parameter, which follows a normal distribution of random numbers with a mean square of 0 and a variance of 1; K is a random number, K∈[-1,1]; f i This represents the current fitness value of the sparrow; f g f represents the current global optimum, i.e., the optimal fitness; wThis represents the current global worst value; ε is the smallest constant to avoid division by zero error.

[0099] It should be noted that, as part of a foraging sparrow population, the watchers will abandon their current activity and move to a new location when danger approaches. Therefore, the global optimal position and best fitness are the result of the watchers' continuous updates.

[0100] SSA possesses excellent global search capabilities, enabling it to find optimal solutions within a large search space, avoiding local minima and improving the model's generalization ability. During the search process, SSA can dynamically adjust its search strategy based on the current search state, making it more computationally efficient than traditional optimization algorithms. It can find satisfactory solutions in a shorter time, making it more convenient for practical engineering applications.

[0101] II. Mixed Mode Decomposition

[0102] An Empirical and Variational Mixed Modal Decomposition (E-VMD) method is proposed to isolate the vehicle-induced response dynamic components. EMD is then used to adaptively decompose the measured strain time history response (bridge anomaly monitoring data x(n)) to obtain multiple intrinsic mode functions (IMF components). The correlation coefficient l1(m) between each IMF component and the bridge anomaly monitoring data x(n) is calculated, where M is the number of IMF components, and a correlation threshold l is defined. limt :

[0103]

[0104] Where ξ is the resolution coefficient; c is an empirical constant, c k In this context, k is the index subscript used to distinguish different sequences after decomposition.

[0105] When l1(m)≥l limt When the m-th IMF component is defined as a useful component, it is defined as a noise component. All useful components are summed to obtain the signal x0(n).

[0106] VMD decomposition is performed on signal x0(n) at different K values, yielding a set of narrowband IMF components (multiple) in each decomposition. The relationship between the narrowband IMF components and signal x0(n) is determined by calculating the correlation coefficient l2(k). The condition l2(k) ≥ l is considered as a subset of the components. limt The narrowband IMF components (k = 1, 2, ..., K) are accumulated to obtain the reconstructed signal x1(n). The mutual information relationship between the preprocessed signal x0(n) and the reconstructed signal x1(n) is calculated using the mutual information method to obtain the mutual information index MI:

[0107] MI[x1,x0]=H(x1)+H(x0)-H(x1,x0) (8)

[0108] Where H(x1), H(x0), and H(x1,x0) are the information entropy and joint entropy of x0(n) and x1(n), respectively, denoted as:

[0109]

[0110]

[0111] in, and Let K be the probability mass function and joint probability mass function of x0(n) and x1(n), respectively. When the mutual information index MI reaches its maximum value, the corresponding K value is the number of optimal modes obtained from the variational mode decomposition of the preprocessed signal x0(n). The optimal number of modes is defined as all x0(n) satisfying l2(k) ≥ l. limt The narrowband IMF components (k = 1, 2, ... K) can be used to obtain the vehicle-induced bridge structural response components.

[0112] III. GRU Neural Network

[0113] A Gated Recurrent Unit (GRU) is a variant of a Recurrent Neural Network (RNN) used for processing time-series data. It addresses the vanishing and exploding gradient problems encountered by traditional RNNs when processing long sequences by introducing a gating mechanism. Compared to Long Short-Term Memory (LSTM) networks, another time-series data processing method, GRU has a simpler gating mechanism while still effectively capturing long-term dependencies in the sequence data. The core of GRU consists of two gating units: the update gate and the reset gate.

[0114] 1. Update the door

[0115] The update gate controls how much information from the previous time step needs to be retained in the current hidden state, and how much information from the current input needs to be added. Its output formula is as follows:

[0116] z t =σ(W z ·[h t-1 ,x t ]+b z (14)

[0117] Among them, z t This indicates the output of the update gate (values ​​range from 0 to 1), h t-1 x represents the hidden state at the previous moment. tW represents the current input. z Let B be the weight matrix. z σ is the bias term, and σ is the sigmoid function.

[0118] 2. Reset the door

[0119] This resets the effect of the previous hidden state of the gate control on the current calculation. It determines whether to "forget" certain irrelevant information. Its output formula is as follows:

[0120] r t =σ(W r ·[h t-1 ,x t ]+b r (15)

[0121] Where, r t W indicates the output of the reset gate. r Let B be the weight matrix. r This is a bias term.

[0122] 3. Candidate Hidden State

[0123] The candidate hidden state is the potential value of the hidden layer at the current time step, which combines the current input and the hidden state at the previous time step (regulated by the reset gate).

[0124]

[0125] in, Represents the candidate hidden state, r t ⊙h t-1 W represents element-wise multiplication (adjusting the hidden state of the previous moment using a reset gate). h Let b be the weight matrix. h This is a bias term.

[0126] 4. Current hidden state

[0127] The current hidden state is dynamically adjusted by balancing the previous hidden state (the hidden state at the previous moment) and the candidate hidden state through the update gate.

[0128]

[0129] Where: h t Represents the hidden state at the current time step, 1-z t z represents the proportion of the previous hidden state that is retained. t This represents the proportion of candidates added to the hidden state.

[0130] GRU uses two gating mechanisms to control the transmission and forgetting of information. The input first passes through an update gate to determine the fusion ratio of new and historical information at the current time step; then, a reset gate controls the influence of historical information when generating candidate states. Next, GRU calculates the candidate hidden state, weights it with the hidden state from the previous time step, and generates the current hidden state, thus completing the processing of time-series information. This structure allows GRU to effectively capture long-term dependencies in time series data while maintaining stable computational efficiency. The GRU neural network is as follows: Figure 1 As shown.

[0131] IV. Combined E-VMD and SSA-GRU Model

[0132] 1. Signal decomposition E-VMD

[0133] Bridge vehicle-induced structural response data collected by sensors in bridge health monitoring systems are often the result of multiple coupled factors, including environmental and sensor influences, making the collected data not an accurate reflection of the bridge itself. Therefore, E-VMD is chosen as the medium for extracting the accurate structural response of the bridge. The E-VMD decomposition method flow is as follows: Figure 2 As shown.

[0134] 2. Anomaly Repair and Optimization (SSA-GRU)

[0135] After obtaining the narrowband IMFs components after E-VMD decomposition, GRU is selected as the main model for time series data repair using the bridge structure response data obtained from E-VMD decomposition. However, considering that the performance of GRU is highly dependent on the selection of hyperparameters, the parameter values ​​obtained by traditional methods relying on experience or continuous trial and error often prevent the model from quickly adjusting to its optimal performance state. To improve the prediction ability and repair accuracy of the GRU model, and considering that the superposition of multiple algorithms may slow down the overall running efficiency of the model, this invention uses SSA to automatically optimize the hyperparameters of GRU. Three parameters that have a significant impact on the training speed and prediction accuracy of the GRU model are selected as optimization objects, with the root mean square error of the prediction results used as the fitness function of the model, until the model performance and stability reach the optimal state. The SSA optimization method for GRU is as follows: Figure 3 As shown.

[0136] 3. Combined E-VMD and SSA-GRU model

[0137] In summary, the method of repairing bridge anomaly monitoring data using the E-VMD and SSA-GRU combined model is as follows: Figure 4 As shown.

[0138] 4. Model Evaluation Indicators

[0139] To verify the proposed model's ability to repair bridge anomaly monitoring data, root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and coefficient of determination (R²) were selected. 2 As an evaluation indicator, the formula is as follows:

[0140]

[0141] Among them, y i For the true value, For predicted values, is the actual average value, and n is the number of samples.

[0142] Among the proposed indicators, the root mean square error (RMSE) is used to measure the average deviation between the predicted and actual values, the mean absolute error (MAE) is used to assess the average absolute error between the predicted and actual values, and the mean absolute percentage error (MAPE) is used to quantify the relative magnitude of the prediction error as a percentage. The smaller the value of the above three evaluation indicators, the higher the accuracy of the model prediction. 2 As a measure of how well a regression model fits the data, its value typically ranges from 0 to 1. When R... 2 The closer the value is to 1, the better the model fits the target. These four evaluation metrics play a crucial role in time series forecasting tasks, objectively quantifying the model's accuracy and stability in predicting the target.

[0143] V. Model Test Study Based on Measured Bridge Anomaly Monitoring Data

[0144] To verify the accuracy, robustness, and generalization ability of the proposed method in repairing bridge monitoring data over time, the experiment used real-time monitoring data of a multi-span simply supported beam bridge as the research object. This bridge is 554.4 meters long, 38 meters wide, and has 22 spans, passing under a railway in a highly complex operating environment. The bridge is equipped with various types of sensors to monitor its health status in real time. The monitored data includes multiple characteristic values ​​such as dynamic strain, displacement, cracks, tilt angle, acceleration, temperature, and humidity, forming a multi-dimensional time series dataset. Low-frequency real-time strain monitoring data of the bridge from August 1st to August 20th, 2024, with a data granularity of 10M, totaling 2880 monitoring data points, were selected. Based on a reasonable ratio of missing data to original data, 1440 data points from the first 10 days were selected for the experiment, and the training and test sets were divided at a 7:3 ratio. The line graphs of all the acquired original data are shown below. Figure 5 As shown.

[0145] 1. Analysis of E-VMD decomposition results

[0146] Using strain monitoring data as the object of E-VMD decomposition, the original signal x(n) is processed according to the working sequence to obtain the decomposition result as follows: Figure 6 As shown.

[0147] The components obtained after E-VMD decomposition exhibit higher regularity, and compared to the raw data collected by the sensor, these components can more effectively reveal the structural characteristics of the data. This decomposition method can accurately extract key information, providing stronger support for subsequent data analysis and repair.

[0148] 2. Missing Signal Prediction and Reconstruction

[0149] Before the experiment, the strain monitoring data after decomposition were normalized:

[0150]

[0151] Among them, X norm The data is normalized, and X is the original data. max X represents the maximum value in the data. min It is the minimum value in the data.

[0152] The parameters for initialization algorithm are set as shown in Table 1.

[0153] Table 1 Initialization Parameter Settings

[0154]

[0155] To verify the proposed model's ability to repair bridge anomaly monitoring data, this invention simultaneously utilizes a single GRU model, an E-VMD combined with a GRU model to compare the proposed model's ability to predict and repair missing bridge monitoring data, and compares the effectiveness of the prediction and repair. Figure 7 It is evident that when predicting and reconstructing strain-related missing data, the curves repaired by the proposed model show a high degree of agreement with the actual curves. The proposed model is better able to learn the temporal features inherent in the training set and achieve relatively accurate prediction and repair based on these features. The agreement, from highest to lowest, is as follows: the E-VMD and SSA-GRU combined model, the E-VMD and GRU combined model, and the single GRU model. Furthermore, the research revealed that selecting appropriate optimization algorithms to optimize the key parameters of the neural network can significantly improve the accuracy of model repair.

[0156] To better verify the model's accuracy, the absolute error between the reconstructed values ​​of the model and the true values ​​on the test set is calculated, and an absolute error plot is drawn. For example... Figure 8As shown, the repair error curve of the single GRU model fluctuates significantly and has low prediction accuracy. The prediction error curve of the GRU model after E-VMD decomposition shows reduced error fluctuation compared to the single GRU model, indicating that E-VMD decomposition can effectively improve prediction accuracy. The combined E-VMD and SSA-GRU model exhibits the smallest error fluctuation and low error values ​​across most time steps, suggesting that SSA optimization can further adjust the parameters of the GRU model, allowing it to better fit the data and thus improve prediction accuracy.

[0157] Based on pre-defined evaluation metrics, the RMSE, MAE, and MAPE of the three models were calculated. Table 2 shows that the MAPE of the proposed combined model on the test set was reduced by 63.79% and 56.84% compared to the single GRU model and the E-VMD / GRU combined model, respectively. It is evident that the proposed model's data repair performance is significantly better than the other two models. Whether considering the training or test set, the values ​​of the three error metrics are the smallest among the three models, indicating that the proposed model possesses high stability and relatively excellent predictive ability.

[0158] Table 2 Comparison of Repair Evaluation Indicators for Each Model

[0159]

[0160] To verify the fitting effect of the proposed model on the strain missing data, the R-values ​​of the reconstructed data and the original data were calculated for each of the three models. 2 Value, such as Figure 9 As shown, the R of the proposed combined model 2 The value reaches 0.99649, demonstrating high fitting accuracy. This proves that the proposed model is significantly superior to the other two insufficiently optimized basic models. Specifically, in terms of prediction performance, the proposed combined model > the E-VMD and GRU combined model > the single GRU model. This is because E-VMD accurately captures the bridge's structural response, improving computational efficiency, more accurately locating frequency components, and enhancing the ability to process nonlinear signals. Simultaneously, SSA accurately optimizes the key hyperparameters of the GRU model, enabling it to better fit the data, thereby improving prediction accuracy and robustness. This makes the proposed model more stable and accurate when handling complex, nonlinear bridge monitoring data, especially in cases of missing data, where it can more effectively repair and reconstruct anomalies.

[0161] In summary, the bridge missing monitoring data repair method based on the E-VMD and SSA-GRU combined model described in the above embodiments accurately acquires the bridge structural response through E-VMD, improving computational efficiency, more accurately locating frequency components, and enhancing the ability to process nonlinear signals. To address the impact of unreasonable hyperparameter values ​​on GRU performance, a sparrow search algorithm is used to optimize key parameters in the GRU neural network, significantly improving the model's robustness and generalization ability, resulting in more accurate and precise repair results. The combined E-VMD and SSA-GRU model achieves a multi-level anomaly data repair framework, fully leveraging the advantages of each component. E-VMD processes nonlinear signals, GRU captures the dependencies between time-series data, and SSA optimizes the GRU neural network, improving its reconstruction performance. This multi-level optimization framework improves the model's prediction accuracy, robustness, and generalization ability.

[0162] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for repairing missing bridge monitoring data based on a combined E-VMD and SSA-GRU model, characterized in that, Includes the following steps: S1: Data Acquisition and Preprocessing Collect bridge anomaly monitoring data of a preset type, and divide the bridge anomaly monitoring data into training set and test set according to a set ratio; S2: Model Building and Training A combined model based on E-VMD and SSA-GRU is constructed. The combined model based on E-VMD and SSA-GRU is trained using training set data to obtain the trained model, namely the bridge missing monitoring data repair model. In the combined model based on E-VMD and SSA-GRU, the actual structural response data of the bridge in the bridge anomaly monitoring data is extracted by the E-VMD method, and the hyperparameters of the GRU neural network are optimized by the SSA algorithm. S3: Missing Data Repair After preprocessing, the real-time collected bridge anomaly monitoring data is input into the bridge missing monitoring data repair model. The bridge missing monitoring data repair model is then used to repair the data, and the repaired bridge monitoring data is output.

2. The method for repairing missing bridge monitoring data based on a combined E-VMD and SSA-GRU model according to claim 1, characterized in that, In step S1, bridge anomaly monitoring data is collected in real time by sensors of the actual bridge health monitoring system.

3. The method for repairing missing bridge monitoring data based on a combined E-VMD and SSA-GRU model according to claim 1, characterized in that, In step S2, the specific process of extracting the bridge structural response from the bridge anomaly monitoring data using the E-VMD method is as follows: S211: The EMD method is used to adaptively decompose the preprocessed bridge anomaly monitoring data x(n) to obtain M IMF components. The correlation coefficient l1(m) between each IMF component and x(n) is calculated, and the correlation threshold l is defined. limt The correlation coefficient l1(m) is greater than or equal to the correlation threshold l. limt The preprocessed signal x0(n) is obtained by adding the IMF components, where m = 1, 2, ... M; S212: Perform VMD decomposition on signal x0(n) under different K values. Each decomposition yields a set of narrowband IMF components. The relationship between the narrowband IMF components and the preprocessed signal x0(n) is determined by calculating the correlation coefficient l2(k). The condition l2(k) ≥ l is considered to be met. limt The narrowband IMF components are added together to obtain the reconstructed signal x1(n), where k = 1, 2, ... K; S213: The mutual information relationship between the preprocessed signal x0(n) and the reconstructed signal x1(n) is calculated by the mutual information method to obtain the mutual information index MI. When the mutual information index MI reaches its maximum value, the corresponding K value is the number of optimal modes obtained by the variational mode decomposition of the preprocessed signal x0(n). S214: Reconstruct all preprocessed signals x0(n) satisfying l2(k)≥l under the optimal number of modes. limt The narrowband IMF component can be used to obtain the actual structural response of the bridge.

4. The method for repairing missing bridge monitoring data based on a combined E-VMD and SSA-GRU model according to claim 3, characterized in that, In step S211, the formula for calculating the correlation coefficient l1(m) is as follows: Relevant threshold l limt The definition is as follows: Where ξ is the resolution coefficient; c is an empirical constant, c k In this context, k is the index subscript.

5. The method for repairing missing bridge monitoring data based on a combined E-VMD and SSA-GRU model according to claim 3, characterized in that, In step S212, the formula for calculating the correlation coefficient l2(k) is as follows: Among them, IMF k This refers to the k-th narrowband IMF component obtained after VMD decomposition. It represents the average value of the k-th narrowband IMF component.

6. The method for repairing missing bridge monitoring data based on a combined E-VMD and SSA-GRU model according to claim 3, characterized in that, In step S213, the formula for calculating the mutual information index MI is as follows: MI[x1,x0]=H(x1)+H(x0)-H(x1,x0) Where H(x1), H(x0) and H(x1,x0) are the information entropy and joint entropy of x0(n) and x1(n), respectively, defined as follows: in, and Let x0(n) and x1(n) be the probability mass functions and the joint probability mass function, respectively.

7. The method for repairing missing bridge monitoring data based on a combined E-VMD and SSA-GRU model according to claim 3, characterized in that, In step S2, the specific process of optimizing the hyperparameters of the GRU neural network using the SSA algorithm is as follows: S221: Set the maximum number of iterations for the SSA algorithm, the number of hidden units, the maximum number of training rounds, and the initial learning rate for the GRU neural network, and use the root mean square error of the prediction results of the GRU neural network as the fitness function. S222: Initialize the sparrow population; S223: Update the positions of the discoverer, joiner, and watcher to obtain the global optimal position and best fitness; S224: Determine if the maximum number of iterations has been reached; S225: If the maximum number of iterations has not been reached, continue iterating and updating, and proceed to steps S223 to S224. Otherwise, output the optimization results of the number of hidden units, the maximum number of training rounds, and the initial learning rate of the GRU neural network to obtain the optimized GRU neural network.

8. The method for repairing missing bridge monitoring data based on a combined E-VMD and SSA-GRU model according to claim 7, characterized in that, In step S223, during each iteration: The location update of the discoverer is described as follows: Where t is the current iteration number; j = 1, 2, 3, ..., d; iter max Indicates the maximum number of iterations; X i,j Let represent the position information of the i-th sparrow in the j-th dimension; α is a random number; R2 is the preset warning value, R2∈[0,1]; ST is the preset safety value, ST∈[0.5,1]; Q is a random number following a normal distribution; L represents a matrix of size 1×d, in which every element is 1; The location update status of new members is described as follows: Among them, Xp is the optimal position currently occupied by the discoverer; The location update status of the vigilant is described as follows: Among them, X best The current global optimal position; β is the step size control parameter; K is a random number, K∈[-1,1]; f i f represents the fitness value of the current individual sparrow; g f represents the current global optimum, i.e., the optimal fitness; w This represents the worst current global fitness value; ε is a constant used to avoid division by zero error.

9. A method for repairing missing bridge monitoring data based on a combined E-VMD and SSA-GRU model according to claim 7, characterized in that, In step S2, the GRU neural network controls the transmission and forgetting of information through two gating mechanisms. When the input bridge real structural response data first passes through the update gate, the fusion ratio of new information and historical information at the current moment is determined. Then, the reset gate controls the degree of influence of historical information when generating candidate hidden states. Next, the candidate hidden states are calculated and weighted together with the hidden states at the previous moment to generate the current hidden state, thereby completing the processing of time series information.

10. A method for repairing missing bridge monitoring data based on a combined E-VMD and SSA-GRU model according to claim 9, characterized in that, In the GRU neural network, the output formula of the update gate is as follows: z t =σ(W z ·[h t-1 ,x t ]+b z ) Among them, z t This indicates updating the output of the gate, h. t-1 x represents the hidden state at the previous moment. t W represents the current input. z Let B be the weight matrix. z Here, σ is the bias term, and σ is the sigmoid function. The output formula for resetting the door is as follows: r t =σ(W r ·[h t-1 ,x t ]+b r ) Where, r t W indicates the output of the reset gate. r Let B be the weight matrix. r For bias terms; The formula for calculating the candidate hidden state is as follows: in, Represents the candidate hidden state, r t ⊙h t-1 W represents element-wise multiplication. h Let b be the weight matrix. h For bias terms; The formula for calculating the current hidden state is as follows: Where: h t Represents the hidden state at the current time step, 1-z t z represents the proportion of the hidden state retained from the previous time step. t This represents the proportion of candidates added to the hidden state.

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